The Gaussian Measure On Algebraic Varieties

Details The Gaussian Measure On Algebraic Varieties The Gaussian Measure On Algebraic Varieties

1998-04-24

arxiv.org/abs/math/9804116v1

Mathematics

Differential Geometry

Latex2.09, 6 pages

Scientific paper

We prove that the ring $\Aff{\R}{M}$ of all polynomials defined on a real
algebraic variety $M\subset\R^n$ is dense in the Hilbert space
$L^2(M,e^{-|x|^2}\de\mu)$, where $\de\mu$ denotes the volume form of $M$ and
$\de\nu=e^{-|x|^2}\de\mu$ the Gaussian measure on $M$.

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